Is there a term for people on the same line of the family tree?

I accidentally confused "generation" and this a long time ago, but now I'm curious.

If two people are both 1st cousins, they are on the same line.

siblings? (or half, or just, 1Qth cousin that is only related to you from the beginning of time)

If you write your WHOLE family tree, and write it organized on ruled paper, the people I am referring to are on the same line.

Generation is exactly the word you want.

A familial generation is a group of living beings constituting a single step in the line of descent from an ancestor

This can be very different from the meaning "a group of people living at the same time" and often was when people had larger families over more years. But it is one meaning of the term, and the only one I have heard of.